Identification of linear time-invariant systems based on initial condition responses

Abstract

Forced responses are commonly used for system identification, but only initial condition responses may be available when a system has no controllable inputs or forced responses cannot be practically measured. It is therefore meaningful to analyse whether initial condition responses can be used to estimate the system matrix. In this work, the identifiability of the nth order (n > 1) linear time-invariant systems from initial condition responses is analysed. Systems with only one measurable state (OMS systems) and those with n measurable states (NMS systems) are considered. Analysis indicates that one initial condition response is not sufficient to uniquely determine the system matrix of an OMS system and n initial condition responses are necessary. The identifiability of an OMS system with data from n independent initial condition responses is equivalent to that of an NMS system with only one initial condition response. Explicit formulations and a non-iterative algorithm are developed for both OMS and NMS systems.